Triplet Superconductor Explorer

NbRe alloy intrinsic triplet superconductivity • Majorana qubit stability • Interactive superconductor comparison
PRL 2025 — Colangelo et al. • NTNU QuSpin • DOI: 10.1103/q1nb-cvh6
Critical Temperature
7 K
NbRe (−266.15 °C)
Pairing Symmetry
Triplet
S = 1, spin-polarized Cooper pairs
Crystal Symmetry
Non-centro.
Broken inversion → singlet-triplet mixing

The Holy Grail of Quantum Materials

In February 2026, physicists at NTNU's QuSpin research center published evidence that the niobium-rhenium alloy NbRe exhibits properties consistent with intrinsic triplet superconductivity — a long-sought material state where superconducting particles carry both charge and spin without resistance.

Unlike conventional singlet superconductors (where Cooper pairs have zero net spin), triplet superconductors form pairs with S = 1, enabling lossless spin transport. This has profound implications for spintronics, quantum computing, and energy-efficient technology.

Key finding: NbRe behaves "completely differently from what we would expect for a conventional singlet superconductor" — exhibiting inverse spin-valve effects characteristic of triplet pairing. Paper selected as PRL Editor's Recommendation.

Why It Matters

⚡
Zero-Loss Spin Transport
Transport spin currents with absolutely zero resistance — enabling ultra-efficient spintronics
🔮
Majorana Fermions
Host exotic quasiparticles that are their own antiparticles — ideal for topological quantum computing
🧊
Practical Tc
Superconducts at 7 K vs ~1 K for other triplet candidates — much more experimentally accessible

Research Team

Lead: Prof. Jacob Linder, NTNU Department of Physics, QuSpin Center (Norway)

Experimental collaborators: Italian group (F. Colangelo et al.)

Device structure: Py/NbRe/Py/α-Fe₂O₃ spin-valve heterostructure

Published: Physical Review Letters (2025), arXiv: 2510.08110

The paper was selected as one of PRL's weekly Editor's Recommendations — a distinction given to roughly 1 in 6 published papers.

Singlet vs Triplet Cooper Pairs

Singlet (S = 0) Conventional superconductors e⁻ ↑ e⁻ ↓ |↑↓⟩ − |↓↑⟩ Anti-parallel spins cancel → No net spin current → Charge transport only Triplet (S = 1) NbRe — spin-polarized pairs e⁻ ↑ e⁻ ↑ |↑↑⟩, |↓↓⟩, |↑↓⟩ + |↓↑⟩ Parallel or symmetric spins → Net spin ≠ 0 → Charge + spin transport

Cooper Pair Symmetry Classification

Superconductivity arises from electron pairing (Cooper pairs) mediated by lattice vibrations or other interactions. The symmetry of the pair wavefunction determines the material's fundamental properties.

Property Singlet (S = 0) Triplet (S = 1)
Total spin 0 (anti-parallel) 1 (parallel/symmetric)
Spin states |↑↓⟩ − |↓↑⟩ |↑↑⟩, |↓↓⟩, |↑↓⟩ + |↓↑⟩
Orbital symmetry Even (s-wave, d-wave) Odd (p-wave, f-wave)
Spin current ❌ None ✓ Lossless
Magnetic field Pair-breaking Can be robust
Majorana modes Requires engineering Intrinsic support
Examples Nb, Al, Pb, YBCO, MgB₂ Sr₂RuO₄(?), ³He, UPt₃, NbRe(?)

BCS Theory & Pairing Mechanism

In BCS theory, electrons near the Fermi surface form Cooper pairs via phonon-mediated attraction. The pair wavefunction must be antisymmetric under exchange:

Ψ(r₁,σ₁; r₂,σ₂) = −Ψ(r₂,σ₂; r₁,σ₁)

For singlet pairing: spin part is antisymmetric, orbital is symmetric (s-wave, d-wave).

For triplet pairing: spin part is symmetric, orbital must be antisymmetric (p-wave, f-wave).

Δ(k) = Ψ_spin × φ_orbital
Singlet: Δ(k) = Δ(−k) [even parity]
Triplet: Δ(k) = −Δ(−k) [odd parity]

Noncentrosymmetric Superconductors

In materials without inversion symmetry, the distinction between singlet and triplet pairing can break down. Asymmetric spin-orbit coupling (ASOC) mixes the two:

H_ASOC = α(k × σ̂) · ẑ
→ Δ = Δ_s + d(k) · σ̂

NbRe is noncentrosymmetric — its crystal structure naturally breaks inversion symmetry, allowing intrinsic singlet-triplet mixing. The key question: how much of the pairing is triplet?

Smoking gun: If the triplet component dominates, the material should show anomalous spin transport behavior — exactly what Colangelo et al. observed in their inverse spin-valve experiment.

The Three Triplet States

A spin-1 Cooper pair has three possible spin projections (ms = −1, 0, +1), described by the d-vector formalism:

|↑↑⟩ m_s = +1 Equal-spin triplet Both spins aligned up Long-range in ferromagnets → Survives exchange field |↑↓⟩ + |↓↑⟩ m_s = 0 Mixed-spin triplet Symmetric combination Short-range proximity → Decays in ferromagnet |↓↓⟩ m_s = −1 Equal-spin triplet Both spins aligned down Long-range in ferromagnets → Survives exchange field
Formula
NbRe
Niobium-Rhenium alloy
Tc
~7 K
vs ~1 K for other candidates
Space Group
P2₁3
Noncentrosymmetric cubic

NbRe Material Properties

Niobium-rhenium is a binary intermetallic compound crystallizing in the noncentrosymmetric α-Mn structure (space group P2₁3). The broken inversion symmetry is crucial — it enables asymmetric spin-orbit coupling (ASOC) that mixes singlet and triplet pairing channels.

PropertyValueSignificance
Crystal structureα-Mn type (P2₁3)Noncentrosymmetric → enables triplet
Tc~7 KHighest among triplet candidates
Nb atomic number41Strong spin-orbit coupling from Re
Re atomic number75Heavy element → large SOC
Upper critical field~12 TExceeds Pauli limit for singlet
Penetration depthType-IIMixed state with vortices

Element Properties

Temperature Comparison

Why Noncentrosymmetric Matters

Centrosymmetric Crystal Inversion symmetry: E(k,↑) = E(−k,↑) → Pure singlet OR pure triplet → Noncentrosymmetric (NbRe) No inversion: ASOC lifts degeneracy → Singlet-triplet mixing allowed!

Inverse Spin-Valve Experiment

The key experiment by Colangelo et al. used a ferromagnet/superconductor/ferromagnet/antiferromagnet (F/S/F/AF) heterostructure to probe the spin-transport properties of NbRe.

Py / NbRe / Py / α-Fe₂O₃ Spin-Valve Device Py (Permalloy) Ferromagnet → M₁ NbRe Superconductor ↑↑ ↑↑ Py (Permalloy) Ferromagnet → M₂ α-Fe₂O₃ (Hematite) Antiferromagnet Substrate

Parallel (P) Configuration

When both Py layers have magnetization aligned in the same direction (M₁ ∥ M₂):

  • Equal-spin triplet pairs (|↑↑⟩) can propagate through both ferromagnets
  • Spin current flows without resistance
  • Critical current is enhanced
  • For singlet: would be suppressed by exchange field
Singlet prediction: Higher Tc in P alignment
Observed: Lower Tc → inverse spin-valve effect!

Anti-Parallel (AP) Configuration

When Py layers have magnetization in opposite directions (M₁ ∥ −M₂):

  • Equal-spin pairs face opposing exchange fields
  • Pair propagation is hindered
  • Less "leakage" of Cooper pairs into the F layers
  • Superconductivity is actually better protected
Singlet prediction: Lower Tc in AP alignment
Observed: Higher Tc → confirms triplet character!

Spin-Valve Effect Simulator

Adjust the angle between magnetizations to see how Tc changes for singlet vs triplet pairing:

0°

θ = 0° (Parallel):

Singlet: Tc is at maximum (pairs protected from exchange field cancellation)

Triplet: Tc is suppressed — equal-spin pairs leak into both F layers

Superconductor Materials Database

Interactive comparison of superconducting materials across pairing symmetry, critical temperature, and applications.

Material Tc (K) Pairing Symmetry Majorana Status

Tc Comparison

Pairing Symmetry Distribution

Triplet Superconductor Candidates — Historical Search

1972
³He superfluid — First confirmed triplet pairing (p-wave) in liquid helium-3. Nobel Prize 2003 (Leggett).
1984
UPt₃ — Heavy fermion superconductor, strong evidence for triplet E₂ᵤ pairing. Tc ≈ 0.53 K.
1994
Sr₂RuO₄ — Initially claimed as chiral p-wave triplet. Decades of debate; now thought to be more complex.
2004
CePt₃Si — First noncentrosymmetric heavy fermion superconductor. Singlet-triplet mixing confirmed.
2011
CuxBi₂Se₃ — Topological insulator doped to superconduct. Evidence for odd-parity (triplet) pairing.
2018
UTe₂ — Spin-triplet candidate with re-entrant superconductivity in extreme fields. Tc ≈ 1.6 K.
2025
NbRe — NTNU/QuSpin reports inverse spin-valve evidence for intrinsic triplet. Tc ≈ 7 K — highest among candidates. PRL Editor's Recommendation.

Majorana Fermions & Topological Quantum Computing

Triplet superconductors are intimately connected to one of the most exciting frontiers in physics: Majorana fermions — particles that are their own antiparticles, first predicted by Ettore Majorana in 1937.

The quantum computing connection: Majorana zero modes in topological superconductors can encode qubits that are inherently protected from local noise — enabling "topological quantum computing" with exponentially lower error rates.

Why Majorana Matters for Qubits

🔒
Topological Protection
Information stored nonlocally across two Majorana modes — immune to local perturbations
🔀
Non-Abelian Braiding
Exchanging Majorana modes performs quantum gates — computation through topology, not precision control
📉
Exponential Error Suppression
Error rate ∝ e−L/ξ where L is separation — errors vanish exponentially with distance

Qubit Architecture Comparison

From NbRe to Majorana Qubits

1. Triplet SC NbRe with intrinsic triplet pairing T_c = 7 K 🧊 → 2. Topological SC Engineer topology via heterostructures or magnetic fields 🌀 → 3. Majorana Modes Zero-energy modes at vortex cores or wire endpoints 🔮 → 4. Topo Qubit Braid Majoranas to perform topologically protected gates 💻

The advantage of NbRe for this roadmap is twofold: (1) intrinsic triplet pairing means less engineering is needed to create topological states, and (2) the relatively high Tc of 7 K makes experiments much more feasible compared to sub-Kelvin candidates like UPt₃ (0.53 K) or UTe₂ (1.6 K).

Error Rate Comparison: Topological vs Conventional Qubits

Adjust the qubit separation to see how error rates scale differently:

5ξ
Transmon Error
~10⁻³
constant (hardware-limited)
Majorana Error
~10⁻³
∝ e−L/ξ
Improvement Factor
1×
exponential scaling advantage

Bibliography

  1. Colangelo, F. et al. "Unveiling Intrinsic Triplet Superconductivity in Noncentrosymmetric NbRe through Inverse Spin-Valve Effects." Physical Review Letters (2025). DOI: 10.1103/q1nb-cvh6
  2. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. "Theory of Superconductivity." Physical Review 108, 1175 (1957).
  3. Sigrist, M. & Ueda, K. "Phenomenological theory of unconventional superconductivity." Reviews of Modern Physics 63, 239 (1991).
  4. Majorana, E. "Teoria simmetrica dell'elettrone e del positrone." Il Nuovo Cimento 14, 171 (1937).
  5. Kitaev, A. Y. "Unpaired Majorana fermions in quantum wires." Physics-Uspekhi 44, 131 (2001).
  6. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. "Non-Abelian anyons and topological quantum computation." Reviews of Modern Physics 80, 1083 (2008).
  7. Bauer, E. & Sigrist, M. Non-Centrosymmetric Superconductors (Springer, 2012).
  8. Ran, S. et al. "Nearly ferromagnetic spin-triplet superconductivity." Science 365, 684 (2019). [UTe₂]
  9. Mackenzie, A. P. & Maeno, Y. "The superconductivity of Sr₂RuO₄ and the physics of spin-triplet pairing." Reviews of Modern Physics 75, 657 (2003).
  10. Smidman, M., Salamon, M. B., Yuan, H. Q. & Agterberg, D. F. "Superconductivity and spin–orbit coupling in non-centrosymmetric materials: a review." Reports on Progress in Physics 80, 036501 (2017).
  11. Linder, J. & Balatsky, A. V. "Odd-frequency superconductivity." Reviews of Modern Physics 91, 045005 (2019).
  12. Sato, M. & Ando, Y. "Topological superconductors: a review." Reports on Progress in Physics 80, 076501 (2017).

Further Reading

📰
Phys.org Coverage
Full article
📰
ScienceDaily
Full article
📄
arXiv Preprint
2510.08110
🏛️
QuSpin Center
NTNU QuSpin